Calculating the Width of Each Section

Oct 13, 2025 by wbrum.org 111 views

Understanding the Problem: A Step-by-Step Approach to Finding the Area of Each Section of the Frame

Introduction

When it comes to finding the area of each section of a picture frame, we need to consider the dimensions of the frame and the inner dimensions of the frame. In this problem, we are given the outer dimensions of the frame as 54 cm x 44 cm and the inner dimensions as 38 cm x 32 cm. Our goal is to find the area of each section of the frame, assuming that the width of each section is the same.

Calculating the Width of Each Section

To find the area of each section of the frame, we first need to calculate the width of each section. Let's denote the width of each section as 'x'. Since the width of each section is the same, we can calculate the width of each section by subtracting the inner dimensions from the outer dimensions.

x = (Outer\ width - Inner\ width) / 2

For the top and bottom sections, the width of each section is:

x = (54 - 38) / 2
x = 16 / 2
x = 8 cm

For the left and right sections, the width of each section is:

x = (44 - 32) / 2
x = 12 / 2
x = 6 cm

Calculating the Area of Each Section

Now that we have the width of each section, we can calculate the area of each section. The area of each section is given by the formula:

Area = Length \* Width

For the top and bottom sections, the area of each section is:

Area = 38 \* 8
Area = 304 cm^2

Since there are two top and bottom sections, the total area of the top and bottom sections is:

Total\ Area = 2 \* 304
Total\ Area = 608 cm^2

For the left and right sections, the area of each section is:

Area = 32 \* 6
Area = 192 cm^2

Since there are two left and right sections, the total area of the left and right sections is:

Total\ Area = 2 \* 192
Total\ Area = 384 cm^2

Conclusion

In this problem, we calculated the area of each section of the picture frame by first finding the width of each section and then using the formula for the area of a rectangle. We found that the area of each top and bottom section is 304 cm^2, and the area of each left and right section is 192 cm^2. The total area of the top and bottom sections is 608 cm^2, and the total area of the left and right sections is 384 cm^2.

Final Answer

The final answer is:

Top and bottom sections: 304 cm^2
Left and right sections: 192 cm^2
Total area of top and bottom sections: 608 cm^2
Total area of left and right sections: 384 cm^2
Frequently Asked Questions: Understanding the Diagram of the Adjacent Picture Frame

Q: What are the outer dimensions of the picture frame?

A: The outer dimensions of the picture frame are 54 cm x 44 cm.

Q: What are the inner dimensions of the picture frame?

A: The inner dimensions of the picture frame are 38 cm x 32 cm.

Q: How do I calculate the width of each section of the frame?

A: To calculate the width of each section of the frame, you need to subtract the inner dimensions from the outer dimensions and divide the result by 2. For the top and bottom sections, the width of each section is (54 - 38) / 2 = 8 cm. For the left and right sections, the width of each section is (44 - 32) / 2 = 6 cm.

Q: How do I calculate the area of each section of the frame?

A: To calculate the area of each section of the frame, you need to multiply the length of the section by its width. For the top and bottom sections, the area of each section is 38 x 8 = 304 cm^2. For the left and right sections, the area of each section is 32 x 6 = 192 cm^2.

Q: What is the total area of the top and bottom sections of the frame?

A: The total area of the top and bottom sections of the frame is 2 x 304 = 608 cm^2.

Q: What is the total area of the left and right sections of the frame?

A: The total area of the left and right sections of the frame is 2 x 192 = 384 cm^2.

Q: What is the total area of the entire frame?

A: To find the total area of the entire frame, you need to add the total area of the top and bottom sections to the total area of the left and right sections. The total area of the entire frame is 608 + 384 = 992 cm^2.

Q: What is the width of the frame?

A: The width of the frame is the difference between the outer width and the inner width. For the top and bottom sections, the width of the frame is 54 - 38 = 16 cm. For the left and right sections, the width of the frame is 44 - 32 = 12 cm.

Q: What is the length of the frame?

A: The length of the frame is the difference between the outer length and the inner length. For the top and bottom sections, the length of the frame is 38 - 32 = 6 cm. For the left and right sections, the length of the frame is 44 - 38 = 6 cm.

Q: How do I find the area of the frame if the width of each section is not the same?

A: If the width of each section is not the same, you need to calculate the width of each section separately and then use the formula for the area of a rectangle to find the area of each section. You can then add the areas of all the sections to find the total area of the frame.

Q: What is the formula for the area of a rectangle?

A: The formula for the area of a rectangle is Area = Length x Width.

Q: What is the formula for the width of each section of the frame?

A: The formula for the width of each section of the frame is x = (Outer width - Inner width) / 2.

Q: What is the formula for the area of each section of the frame?

A: The formula for the area of each section of the frame is Area = Length x Width.

Q: How do I find the total area of the frame if the width of each section is not the same?

A: If the width of each section is not the same, you need to calculate the area of each section separately and then add the areas of all the sections to find the total area of the frame.